Question: $A$ $B$ $C$ If: $ AC = 23$, $ AB = 2x + 2$, and $ BC = 3x + 6$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {2x + 2} + {3x + 6} = {23}$ Combine like terms: $ 5x + 8 = {23}$ Subtract $8$ from both sides: $ 5x = 15$ Divide both sides by $5$ to find $x$ $ x = 3$ Substitute $3$ for $x$ in the expression that was given for $BC$ $ BC = 3({3}) + 6$ Simplify: $ {BC = 9 + 6}$ Simplify to find ${BC}$ : $ {BC = 15}$